Please help me answer questions #1-2 on page 108. In addition, provide steps for each answer. In this lab, we compared different substances heat and cool at different rates. We heated ethanol and water and cool it in an ice bath. We then compare the two and analyze the differences. Data will be given below.

Report: Experiment 9: Name_ Date_ Laboratory Instructor Lab Day & Time 1. Calculate averages and standard deviations. Use Equation (4): 2. Graph the plot Temperature vs time. This will show you the cooling curve. For best results, graph using Microsoft Excel. Add an exponential trend-line and select show equation. Observe another form of Equation 3: In(T - To) = kt + C T - To = Cekt T = Cekt + To 108Lab 9 Data Averages will be given to save you the trouble of averaging three sets of data. Water: Time (s) temperature (C) 55 10 40 20 32.3 30 27 40 22 50 19.3 Ethanol: Time (s) temperature (C) 55 10 44.3 20 32.6 30 27.3 40 23.3 50 20.3Learning Objectives: As you work through this assignment you will: . Apply safety protocols for alcohol (toxic fumes and do not exceed 60'C). Learn principles of thermodynamics. Explore principles of thermodynamics both through experimentation and quantitatively. Introduction: The Second Law of Thermodynamics is the closest statement that all of science has as an absolute truth. It states that the total entropy of a system can never decrease over time. While one reaction may decrease the entropy of a system, subsequent reactions will eventually increase the entropy and exceed the initial decrease. While on the surface this seems fairly straightforward, the implications of this assertion provides the framework for nearly everything else in thermal dynamics particularly in regard to directionality, such as that heat will always move from high to low. Newton's Law of cooling models this quite well with the differential Equation (1). (1) dT/dt = k(T - To) which means that the rate of temperature change (dT/dt = Kelvins/sec) is directly proportional (k) to the difference between the current temperature of the system (T) and the temperature of its surroundings (T.). Before making this equation more manageable, it is important to understand the natural function ex. This is a powerful function with the base of e, being Euler's number (not to be confused with Euler's constant) and is the solution to the infinite series 1l. This function is useful because the derivative of the function (the slope of the function on a graph) is equal to itself. In other words, it is a function that changes in proportion to itself and thus is useful for modeling natural systems. For example, in one year a family might have one child whereas 100 families can have 50+ children, or 1000 families, 500+ children which means that the rate a population changes is directly proportional to the number of people in the current population. Population modeling, 104compound interest, thermal dynamics, and anything else that changes this way can be modeled using this one function. So Equation (2)... dT - = k(T - To) dT ( T - T . ) kat (2) In(T - To) = kt + C This solution follows the form y = mx + b, the equation of a line, where In(T-To) is the natural log of the difference between the temperature of the system at a time and the temperature of the surroundings, To. The proportionality constant is the relationship between the changing temperature and time and C is the natural log of the initial temperature difference. Consider the following problem... It takes 10minutes for a metallic mass to cool from 120 degrees Celsius to 71 Celsius in a container having an ambient temperature of 43 degrees Celsius. What is the time necessary for this object's temperature to cool to 50 degrees from 120 degrees? The exponential counterpart of Equation (2) is Equation (3): (3) T(1) = I. + (T_.- The# Using Equation (3) and the information from the problem we can solve for the constant (k)... T() -T. + (Todmar - Tje" = 71 =43+(120-43)e- = 28=77e-104 28 77 In =-10k Ine' k = - In -0.10 105The question asks for the time it takes to cool to room temperature so we again use (3). T(1)- T. +(Tutor -T. )e- - 50 - 43+(120-43) 7-77el - In(- -0.101 - 0.10 1 In -24 min Could you calculate the time the mass would take to cool down to room temperature? Do it. [Find this question at the end of the report section.) Procedure: Materials: 16. test tube 17. water (hot and cold) 18. thermometer Set Up: Fill a test tube with 5ml of water. Insert a thermometer into a one-holed stopper and close the tube. Prepare an ice bath. Add an additional beaker of water (no ice) into the bath with a thermometer. Also prepare a heat bath and set to ~55"C.Carefully warm the tube to 55"C. Do not exceed 75'C and do not heat too quickly or the stopper will pop. Note: Point the end of the test tube away from people. Carefully measure the temperature of the bath and the water sample. Place the warmed water sample into the water beaker as deep as you can without submerging. Record the temperature of the water sample every 10 seconds until it approaches the temperature of the water beaker while stirring the cold water. Repeat this experiment two more times. Be careful to have the water sample starting temperature the same as in the first trial. The same applies for the water beaker sample. You will need Equation (4) for error analysis. (4) 0=14 n-1 106